Putin Accountability Act This bill imposes sanctions pertaining to Russia and addresses related issues. The President must impose sanctions, with some exceptions, on individuals and entities that knowingly and directly provide specialized financial messaging services to Russia's central bank (or enables access to such services); entities responsible for constructing, financing, or operating Nord Stream 2 (a pipeline constructed to increase Russian natural gas exports) and the corporate officers and controlling shareholders of such entities; individuals and entities in Russia involved in kleptocracy, Russian government activities to subvert U.S. democratic institutions and interests, or Russian government disinformation campaigns against the United States; and entities that are Russian state development corporations, as well as any officials of such an entity. The President must impose property-blocking sanctions on such individuals and entities and also visa-blocking sanctions on the individuals. The President must also (1) issue regulations to prohibit U.S. individuals and entities from dealing in Russian sovereign debt; and (2) issue a determination as to whether certain specified Russian individuals meet the criteria to be subject to sanctions under various authorities, including this bill. The Department of State must (1) designate Russia a state sponsor of terrorism, and (2) report to Congress a determination of whether Russia-affiliated armed entities in the Donbas region of Ukraine meet the criteria to be designated as foreign terrorist organizations. The bill prohibits expending funds to engage with Russia's government on cyber issues or arms control negotiations until certain conditions have been met.